COOK THE ONIONS AND MUSHROOMS. In a heavy-bottom 4-quart sauce pan, heat the olive oil over medium heat. Add the onion, and sauté until the onion is soft and translucent, about 10 minutes.

Add the garlic and a pinch of salt, and sauté until the onion begins to turn brown and soft, about 5 minutes.

ADD THE MUSHROOMS and cook, stirring and scraping the bottom of the pan, until the mushrooms are browned, about 5 minutes.

ADD THE TOMATO PASTE, RED WINE, AND HERBS. Add the tomato paste, continuing to stir and scrape the bottom of the pan. Then add the red wine, thyme, parsley, bay leaf, and peppercorns.

Cook at a low boil (lots of small bubbles just breaking the surface of the sauce) until the sauce has been reduced by one-quarter (to about 3 cups). This will take about 15 minutes and is the first reduction. (It’s still a thin sauce; it won’t thicken until you add the roux.)

ADD THE MUSHROOM ESSENCE, and cook at a low boil until reduced by one-quarter again (to about 5 1/2 cups), about 15 minutes. (This is the second reduction).

MAKE A ROUX. Meanwhile, melt the butter in a small skillet over medium heat. Add the flour, and stir until the mixture is light brown and smells toasty. Set aside to cool.

ADD THE MEDEIRA. After the sauce has been reduced the second time, add the Madeira, lower the heat, and simmer the sauce for 10 minutes.

STRAIN THE SAUCE. Remove from the heat, and pour the thin sauce through a mesh strainer into another saucepan, pressing the solids with the back of a large spoon. You should have about 4 cups strained sauce. Discard the solids in the strainer.

ADD THE ROUX. Bring the strained sauce to a simmer until the lumps disappear and the sauce begins to thicken. Season to taste with the salt and pepper, and keep warm over low heat for up to 15 minutes. If you’re going to hold the sauce any longer than that, refrigerate and reheat over medium-low heat.

Chef Suggestions

Start this sauce by first making a rich mushroom broth, mushroom essence, a process that takes an hour or more to complete.